Why are the Dead not mentioned here?
As for The Who, they are very influential. There's no Pearl Jam or Kiss without The Who. I would argue that the first two Alice Cooper albums (now that I'm an expert, because I listened to them twice each, hahahah!) are heavily influenced by The Who, at least vocally and arrangement-wise.
For me:
1. Beatles
2. Zeppelin
3. Stones
4. Floyd
5. The Who
6. The Grateful Dead
7. Jimi Hendrix
8. Black Sabbath
American Only:
1. The Grateful Dead
2. Aerosmith
3. Kiss
4. Van Halen
Yes, I know Hendrix is American; I purposefully excluded him, though, because he wasn't "quintessentially" American, and I didn't want to have to decide between 3, 4, and 5. The Dead, with their love of Bluegrass and Americana was perhaps the quintessential American band. Aerosmith billed themselves as the "American Stones". Kiss is about as American - in every way, good and bad - as you get. Van Halen is the blueprint for almost the entire LA - read: American - metal scene, which goes on to this day.